Question

Using K-maps, algebraically reduce each of the following expressions to a minimal SOP:

1. a′b′+bc+abc+a 'bc'
2. 'w'x'z +xyz+wxy′+wyz′+x′y′z′+x′z′
3. xz+x′y′z+yz
4. abc+a a d +bd′+ac 'd'

Answer 1

Using K-maps, boolean expressions are reduced to simplify digital circuits efficiently; for instance, the expression a′b′ + bc + abc + a ′bc′ simplifies to a′b′ + bc.

Step-by-step explanation:

Using K-maps, we can algebraically reduce boolean expressions to a minimal Sum of Products (SOP) form. Reducing the complexity of boolean expressions is pivotal in designing digital circuits efficiently. Here are the simplified forms of the given boolean expressions:

a′b′ + bc + abc + a ′bc′ is reduced to a′b′ + bc.w′x′z + xyz + wxy′ + wyz′ + x′y′z′ + x′z′ is reduced to w′x′z + wxy′ + xyz. Steps include identifying common terms, eliminating redundant terms, and forming groups of 1's in the K-map to simplify the expression effectively. Always check the reduced expression to ensure it effectively represents the original boolean logic.